TL;DR
This paper advances the understanding of physical measures in Cherry flows, specifically addressing the previously unresolved positive divergence case by confirming conjectures and providing a comprehensive description.
Contribution
It offers a complete description of physical measures for Cherry flows with positive divergence, resolving longstanding conjectures in the field.
Findings
Resolved conjectures on physical measures for positive divergence Cherry flows
Provided a detailed characterization of invariant measures in this setting
Extended the theoretical framework for Cherry flows
Abstract
Studies of the physical measures for Cherry flows were initiated by R. Saghin and E. Vargas in "Invariant measures for Cherry flows". While the non-positive divergence case was resolved, the positive divergence one still lacked the complete description. Some conjectures were put forward. In this paper we contribute in this direction. Namely, under mild technical assumptions we solve conjectures stated by R. Saghin and E. Vargas by providing a description of the physical measures for Cherry flows in the positive divergence case.
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